Sometimes, when working with infinite series, it's useful to add "dilated" or "translated" versions of the infinite series, term by term, back to the original. There are ways of making this rigorous ...

If $f(n)$ is an arithmetic function with $|f(n)|=1$, and $$\lim_{s\to+1} (s-1)\sum_{n=1}^\infty\frac{f(n)}{n^s}=0$$
Can I deduce that $$\lim_{s\to +1}(s-1)^2\sum_{n=1}^\infty\frac{f(n)\ln(n)}{n^s}=0$$
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Let $s \in C$. Let $D = A[[n^{-X}]]$ be a subring of the formal (or absolutely converging on a region; whatever is needed) Dirichlet series with base ring $A$. Define a minimal Dirichlet series for ...

With the help of Raymond Manzoni and Greg Martin I was able to derive an explicit formula for the number of primes of the form $4n+3$ in terms of (sums of) sums of Riemann's $R$ functions over roots ...

I have encountered a sequence which involves both some multiplicative arithmetic functions and argument shifts and does not seem to fit neither into Dirichlet nor Lambert kind of generating function. ...

Let $\Omega(n)$ and $\omega(n)$ be the number of prime factors of $n$ and of distinct prime factors of $n$, respectively.
The Dirichlet G.F of $2^\omega$ is well known, and I was wondering if that of ...

I read that the Dirichlet function (1 if Rational, 0 else) can be written as:
What is the proof of that? Are those limits commutative? Is there any other closed formula for Dirichlet function? (With ...